Why order of quote character "'" in relation to '#1=' matters in circular lists?

I am experimenting with circular lists and have written a flawed graph viewer. So when I try to draw 2 different graphs

(graph-viewer:graph '#1=(1 2 3 #1#) "a")
(graph-viewer:graph #1='(1 2 3 #1#) "b")

I get who different pictures with the latter version having a quote symbol included in the graph.

You need to think how the reader does its job.

When it sees #1=, it knows to store whatever comes next and re-use it on #1# - think about it as a "binding" for the "variable 1".

When it sees '<blah>, it reads it as (quote <blah>).

Thus, when it sees '#1=(1 2 3 #1#), it reads it as

(quote (1 2 3 *))
       ^      |
       |      |
       +------+

(quote is outside of "binding of 1")

while #1='(1 2 3 #1#) is read as

(quote (1 2 3 *))
^             |
|             |
+-------------+

(quote is inside the "binding of 1").

The "arrow" in the pics above is the reference, i.e., * points along the arrow.